How can I make an object appear or disappear smoothly?
You can use the node editor to animate the mix shader slider.
this shouldn't matter what render engine your are in.

Here are two examples posted:

 &lt;-- Blender Render (Blender Internal)

 &lt;-- Blender Cycles

Here are the file links for you to see how it is done:

&lt;-- Blender Render

&lt;-- Blender Cycles

Hope it helps - Kind Regards,

RRiggs



Added in response to the comments below:

To make this a little more expressive without having to download files, here is the summary of what I would do: 

The 1st question was - how to make an object gradually appear/go away. 

The second one is how to do this with a texture. 

The quick answer is (IMHO), add two materials to each of the objects, one of those materials needs to be completely transparent, and the other material needs to be the desired visible one. 

For the second part of the question: 

Two textures will be needed for each of the objects that require the texture differences. 

In either case the 'mix' sliders within the node editor can be key-framed in the timeline by hovering your mouse over them and hitting the I key.

Your control over the timeline and keyframes allow you to have the control over how gradual you want the effect to be.